Tanev gets a six-year deal with an annual average value of $3.5 million.
The 28-year-old Tanev has seen an increase in playing time and production over the course of his four seasons in the NHL, all with Winnipeg. He had 14 goals and 15 assists while averaging 14:07 in ice time over 80 games last seasons -- all career highs.
Tanev is also a physical player, as his 278 hits in 2018-19 were the third-most in the NHL. He did so while drawing just 41 penalty minutes, which tied for 97th in the league.
He was an unrestricted free agent for the first time after playing for the Jets on a series of one-year deals since joining the team in 2016.
Pittsburgh traded Kessel to the Coyotes.
"The signing of Tanev was really good for us," Penguins general manager Jim Rutherford said. "Everyone in the organization thinks really highly of him. He's a really good skater, a good penalty killer. He is a guy that makes the team harder to play against."
Rutherford downplayed the length of Tanev's deal, chalking it up to the cost of doing business.
"It's the way things work on July 1," Rutherford said. "You either give the player close to what he wants or you don't get the player. We felt so strong about Tanev that we were willing to go as far as we had to go to make sure we got him."
Tanev will likely be the only splashy signing by the salary cap-strapped Penguins during free agency, which should give Rutherford time to get to the next item on his list: extending the contract of coach Mike Sullivan. Sullivan, who led Pittsburgh to consecutive titles in 2016 and 2017, is entering the final year of his current deal.
"I feel Mike is a terrific coach," Rutherford said. "He's done a very good job here. He has good communication with the players and I would like to see him stay long-term. But when I get to that, I don't know."
Information from The Associated Press was used in this report.